结合无下采样Shearlet模极大值和改进尺度积的有噪图像边缘检测

为从噪声污染的图像中提取出更为清晰、连续的边缘，进一步改善边缘检测效果，本文提出了一种基于无下采样Shearlet模极大值和改进尺度积的边缘检测方法。首先对含噪图像进行多尺度、多方向无下采样Shearlet变换（Non-subsampled Shearlet Transform, NSST），得到图像在NSST域的高频系数；然后选取相邻的两个较大尺度的高频系数进行改进的尺度积运算，并经NSST模极大值处理得到边缘二值图像；最后使用区域连通方法去除二值图像中的孤立点，得到准确的边缘图像。大量实验结果表明，与小波模极大值、小波尺度积、基于无下采样Contourlet变换（Non-subsampled Contourlet Transform, NSCT）模极大值和尺度积、NSST模极大值等4种边缘检测方法相比，本文提出的方法具有更强的抗噪能力，且有效地避免了纹理的影响，检测出的边缘完整清晰，连续性好。 

Edge Detection of Noisy Images Combining Modulus Maxima with Improved Scale Product of Non-subsampled Shearlet Transform

In order to extract clearer and more continuous edges from a noise-contaminated image, and further improve the effect of edge detection, a method of edge detection is proposed based on modulus maxima and improved scale product of non-subsampled shearlet transform. Firstly, the multi-scale and multi-direction decomposition of noise-contaminated image is performed through non-subsampled shearlet transform (NSST) to get the high-frequency coefficients in NSST domain. Then the high-frequency coefficients in two adjacent larger scales are selected for the improved multi-scale product operations, and the NSST modulus maxima processing is carried out to get the binary image of edges. Finally, the isolated points are removed according to the regional connectivity and the accurate edge image is obtained. The simulative experimental results show that, compared with four edge detection methods (wavelet modulus maxima method, wavelet scale product method, non-subsampled contourlet transform (NSCT) modulus maxima and scale product method, NSST modulus maxima method), the method proposed in this paper has stronger ability of resisting noise, and the influence of texture is avoided effectively. The detected edges are clear, complete and with high continuity.